The diagram shows a right-angled triangular prism. Work out the volume of the prism.

The base of the prism is a right-angled triangle with a base of 7 cm and a height of 4 cm.
The formula for the area of a triangle is $A = \frac{1}{2} \times \text{base} \times \text{height}$.

$$A_{base} = \frac{1}{2} \times 7 \text{ cm} \times 4 \text{ cm}$$ $$A_{base} = \frac{1}{2} \times 28 \text{ cm}^2$$ $$A_{base} = 14 \text{ cm}^2$$

The formula for the volume of a prism is $V = \text{Area of base} \times \text{Length}$.
The length of the prism is given as 12 cm.

$$V = 14 \text{ cm}^2 \times 12 \text{ cm}$$ $$V = 168 \text{ cm}^3$$

The volume of the prism is $168 \text{ cm}^3$.